RX Qubit (Resonant Exchange)

Figure

Description

The resonant-exchange (RX) qubit is a three-electron, triple-quantum-dot spin qubit operating with always-on exchange coupling and driven by resonant RF modulation near the qubit splitting. It encodes in the $S=1/2$ subspace of three electrons, using the two degenerate $S_z=+1/2$ doublet states distinguished by their symmetry under exchange of the outer dots.

Unlike pulsed exchange-only qubits that require large, abrupt detuning pulses to switch couplings on and off, the RX qubit operates at a symmetric operating point ($J_{12}\approx J_{23}$) where the exchange-defined splitting creates a static energy gap $\hslash {\omega }_q$. Single-qubit rotations are then performed by resonantly driving at frequency ${\omega }_d\approx {\omega }_q$, analogous to electron spin resonance but using exchange modulation rather than magnetic fields.

This operating mode provides partial protection against low-frequency charge noise: at the symmetric point, the qubit frequency is first-order insensitive to detuning fluctuations (a sweet spot). The tradeoff is that the qubit is always precessing, requiring phase-locked resonant control rather than simpler DC pulsing.

Hamiltonian

Low-energy effective qubit model in the rotating frame:

$H=\frac{\hslash {\omega }_q}{2}{\sigma }_z+A_{\text{RF}}\cos ({\omega }_{d}t){\sigma }_x$

where ${\omega }_q$ is set by the static exchange couplings among the three dots. The qubit splitting at the symmetric point is:

$\hslash {\omega }_q\propto \sqrt{J_{12}^2+J_{23}^2-J_{12}{J}_{23}}$

which at $J_{12}=J_{23}=J$ gives $\hslash {\omega }_q\propto J$.

Motivation

• Preserves the all-electrical, exchange-only control advantage — no micromagnets or magnetic field gradients needed.
• Operates at a charge-noise sweet spot, improving coherence over non-resonant exchange-only pulse sequences.
• Provides a practical bridge between exchange-only and AEON-type operation for three-spin encodings.
• Compatible with resonator-mediated long-range coupling proposals for scaling beyond nearest-neighbor interactions.

Experimental Status

First demonstration — Medford et al. (2013):

• Demonstrated coherent resonant-exchange qubit operation in a GaAs triple quantum dot.
• Showed resonant driving at the exchange-defined splitting frequency.
• Observed Rabi oscillations and characterized the sweet-spot protection.

Continued development (2013–present):

• Demonstrated self-consistent measurement and state tomography of exchange-only qubits using resonant techniques (Medford et al., Nature Nanotechnology, 2013).
• Si/SiGe implementations of three-spin qubits have shown improved coherence over GaAs.
• Integration with resonator coupling for long-range interactions remains an active area.

Key Metrics

Metric	Value	Notes	Fidelity reference
1Q gate fidelity	98–99.9%	Device and material dependent	Gyenis et al. 2021
Qubit splitting	1–10 GHz	Set by static exchange couplings	—
2Q coupling path	Exchange / resonator-mediated	Architecture dependent	—
Operating temperature	20–100 mK	Semiconductor dilution setups	—

References

Original proposal

• J. Medford et al., “Quantum-Dot-Based Resonant Exchange Qubit,” Phys. Rev. Lett. 111, 050501 (2013)

Experimental demonstrations

• J. Medford et al., “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotech. 8, 654 (2013)

Related review

• A. Gyenis et al., “Moving beyond the Transmon: Noise-Protected Superconducting Quantum Circuits,” PRX Quantum 2, 030101 (2021)

Linked Papers

• medford-2013-rx-qubit

Related Entries

• exchange-only-qubit — parent encoding; RX is the resonantly driven variant
• aeon-qubit — always-on exchange qubit with related operating principles
• singlet-triplet-qubit — two-electron spin qubit; simpler encoding, similar materials